PLANT CAPITAL COST ESTIMATION VIA SCALING FACTOR

Given that the total capital investment (TCI) of a 50,000-ton/year polypropylene unit is $60,000,000 (in 2002 dollars), find the TCI required for a 75,000-ton/year polypropylene unit via the scaling factor method.

Calculation Procedure
1. Apply the appropriate power-function formula. In the scaling factor method, the TCI is estimated via the following formula (a power function):
TCI2 = TCI1(C2/C1)E
where TCI1 and TCI2 = total capital investment of existing and planned unit, respectively, in dollars
TCI1 = $60,000,000
C1,C2 = capacity of existing and planned unit, respectively, in tons/year
C1 = 50,000 and C2 = 75,000
E = scaling exponent = 0.70

Thus
TCI2 = 60,000(75,000/50,000)0.70 = $80,000,000 (rounded)

Related Calculations. The scaling factor method is an appropriate procedure for estimating the TCI only under the following conditions:

1. The existing and planned units are identical (or nearly so), in terms of processing steps, end products, major equipment items used, and other respects.

2. The desired estimate falls within the category of “order-of-magnitude/screening/scoping” cost estimates (i.e., those estimates with a presumed accuracy less precise than ±30%).

3. The capacity of the planned unit falls within the capacity range for which the scaling exponent is valid. Rarely is the power function relationship between TCI and capacity a smooth curve over the entire capacity range.

Typically, the scaling exponent increases in value with increasing capacity. However, as the scaling exponent approaches unity, it becomes less costly to build two units, each with half the capacity of the large plant, than to construct a single, large-capacity plant.

4. The costs of both the existing and planned units are expressed in dollars of the same period. In this example, the TCIs are in 2002 dollars. If the costs are not of the same vintage, the cost of the existing plant (which is likely older) will have to be adjusted to the same year dollars as that of the planned unit.

However, unless the cost vintages are much different (e.g., five years or more), adjustments for escalation would be “fine tuning,” compared to the relative inaccuracy of these scaling factor estimates.

DETERMINING THE LABORATORY-REACTOR SIZE NEEDED FOR SEEDING A BIOLOGICAL REACTION

SIZING OF BIO-REACTOR EXAMPLE AND TUTORIALS

Assuming a minimum 12% inoculum volume, what size of laboratory vessel would be required to initiate the seeding of a 20,000-L full-scale cell-culture bioreactor?

Calculation Procedure

1. Determine the size of reactor that would be required to seed the 20,000-L bioreactor. Since the seed volume must represent 12% of the vessel before reaction starts, the bioreactor being specified in this step would have to have a size 12% that of the 20,000-L bioreactor, or (0.12)(20,000), or 2400 L.

2. Determine the size of bioreactor needed to seed the 2400-L bioreactor of Step 1. Applying the same logic as in step 1, we see that the bioreactor being sought in this second step must be sized at 12% of 2400 L, or (0.12)(2400), or 288 L.

3. Repeat Step 2 successively until a bioreactor of reasonable laboratory volume is reached. Twelve percent of 288 L is 34.6 L; then, 12% of 34.6 is 4.15 L; and 12% of 4.15 L is 500 ml. Thus, a 4.15-L laboratory vessel can be used if available.

Otherwise, use a 500-ml vessel. The contents of the 500-ml vessel provide seeding for the 4.15-L vessel; the contents of the latter vessel then seed the 34.6-L bioreactor; the contents of this latter then seed the 288-L bioreactor; and so on.